Staff: Mentor

Bernoulli's principle relates the pressure, velocity, and height between two points along a fluid under certain conditions (such as incompressible, steady flow, non-viscous). It is a statement of conservation of energy along the fluid.

If you restrict the space which air can take up (by putting a wing in its path, for instance), the temperature rises, the density increases, and the pressure rises. According to thermodynamic properties, how much each changes depends entirely on the Mach number.

For low Mach number flows (less than .3), the density changes less than 5%, so it can be safely modeled as incompressible. For high Mach numbers (modern aircraft or rocket nozzles), using Bernoulli will give you very wrong numbers. In those cases, the more complicated thermodynamic properties must be used. If you're interested, Introduction to Flight, by John D. Anderson is a very well written textbook which has a chapter or three on it.

Examine the equation the first thing to note is that the 2 sides only differ by the subscripts, this means it is relating the same properties in different regions.

The first term is a P or pressure, since all the terms are added they must all have the units of pressure. The second term is the density times the square of the velocity, this looks suspiciously like a kinetic energy. Notice that Doc Al mention conservation of energy? So this expression corresponds to a pressure due to the motion of the fluid. The last expression is a similar to a potential energy, this is a pressure due to fluid depth.